SUMMARY

SUMMARY

In this chapter, you have studied the following points:

1.Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.

2.A quadratic polynomial in x with real coefficients is of the form ax² + bx + c, where a, b,c are real numbers with a\(\ne\)0.

3.The zeroes of a polynomial p(x) are precisely the x-coordinates of the points, where the graph of y = p(x) intersects the x - axis.

4.A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.

5.If \(\alpha\) and \(\beta\) are the zeroes of the quadratic polynomial ax² + bx + c, then \(% MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey % 4kaSIaeqOSdiMaeyypa0JaeyOeI0YaaSaaaeaacaWGIbaabaGaamyy % aaaacaGGSaGaeqySdeMaeqOSdiMaeyypa0ZaaSaaaeaacaWGJbaaba % Gaamyyaaaaaaa!44BC! \alpha + \beta = - \frac{b}{a},\alpha \beta = \frac{c}{a}\).

6.If \(% MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaai % ilaiabek7aIjaacYcacqaHZoWzaaa!3C3D! \alpha ,\beta ,\gamma \) are the zeroes of the cubic polynomial ax³ + bx² + cx + d, then

7.The division algorithm states that given any polynomial p(x) and any non-zero polynomial g(x), there are polynomials q(x) and r(x) such that

p(x) = g(x) q(x) + r(x),

where      r(x) = 0 or degree r(x) < degree g(x).